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For over 2000 years the construction of a regular heptadecagon (17 sided polygon) eluded the world’s finest mathematicians.
That was until 1796 when a brilliant 19 year old prodigy named Carl Friedrich Gauss proved that the regular 17-gon was indeed constructible using only a compass and straight edge.
Now, regarded by many as the greatest mathematician of all time, he pioneered discovery in number theory, geometry, algebra, physics, astronomy and statistics.
It is believed Gauss never actually constructed the heptadecagon himself, instead publishing his mathematical proof for others to translate into physical construction.
In this video I demonstrate an elegant approach by H. W. Richmond from 1893. Although entirely constructible using only the classic tools of Greek Geometry, I use the computer for speed and precision.
It is said that Gauss was so proud of his work that he requested the heptadecagon be inscribed on his tombstone. The stonemason declined on the account it would be indistinguishable to a circle.
However, If you look closely on the base of a monument to him in Brunswick, Germany, you can see a golden 17 pointed star known as a heptadecagram.
Music: Foria - Break Away [NCS Release]
Software: Geogebra (and it's completely free :))
Erratum: the caption at 4:32 should read 2 d.p. not 2 s.f. but hey, we all make mistakes :). To be precise, each interior angle is exactly 158 14/17.